Import Libraries

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import seaborn as sns
import warnings
warnings.filterwarnings('ignore')

from sklearn.cluster import KMeans
from sklearn.decomposition import PCA 
from sklearn.metrics import silhouette_score
from sklearn.preprocessing import StandardScaler, MinMaxScaler

Import Data

df = pd.read_csv('flight.csv', delimiter=',')
df.head(10)

	MEMBER_NO	FFP_DATE	FIRST_FLIGHT_DATE	GENDER	FFP_TIER	WORK_CITY	WORK_PROVINCE	WORK_COUNTRY	AGE	LOAD_TIME	...	SUM_YR_2	SEG_KM_SUM	LAST_FLIGHT_DATE	LAST_TO_END	AVG_INTERVAL	MAX_INTERVAL	EXCHANGE_COUNT	avg_discount	Points_Sum	Point_NotFlight
0	54993	11/2/2006	12/24/2008	Male	6	.	beijing	CN	31.0	3/31/2014	...	234188.0	580717	3/31/2014	1	3.483254	18	34	0.961639	619760	50
1	28065	2/19/2007	8/3/2007	Male	6	NaN	beijing	CN	42.0	3/31/2014	...	167434.0	293678	3/25/2014	7	5.194245	17	29	1.252314	415768	33
2	55106	2/1/2007	8/30/2007	Male	6	.	beijing	CN	40.0	3/31/2014	...	164982.0	283712	3/21/2014	11	5.298507	18	20	1.254676	406361	26
3	21189	8/22/2008	8/23/2008	Male	5	Los Angeles	CA	US	64.0	3/31/2014	...	125500.0	281336	12/26/2013	97	27.863636	73	11	1.090870	372204	12
4	39546	4/10/2009	4/15/2009	Male	6	guiyang	guizhou	CN	48.0	3/31/2014	...	130702.0	309928	3/27/2014	5	4.788079	47	27	0.970658	338813	39
5	56972	2/10/2008	9/29/2009	Male	6	guangzhou	guangdong	CN	64.0	3/31/2014	...	76946.0	294585	1/13/2014	79	7.043956	52	10	0.967692	343121	15
6	44924	3/22/2006	3/29/2006	Male	6	wulumuqishi	xinjiang	CN	46.0	3/31/2014	...	114469.0	287042	3/31/2014	1	7.190000	28	20	0.965347	298873	29
7	22631	4/9/2010	4/9/2010	Female	6	wenzhoushi	zhejiang	CN	50.0	3/31/2014	...	114971.0	287230	3/29/2014	3	10.111111	45	7	0.962070	351198	14
8	32197	6/7/2011	7/1/2011	Male	5	DRANCY	NaN	FR	50.0	3/31/2014	...	87401.0	321489	3/26/2014	6	13.054545	94	5	0.828478	295158	7
9	31645	7/5/2010	7/5/2010	Female	6	wenzhou	zhejiang	CN	43.0	3/31/2014	...	60267.0	375074	3/17/2014	15	11.333333	73	13	0.708010	251907	16

10 rows × 23 columns

Exploratory Data Analysis

Descriptive Analysis

eda = df.copy()

eda['MEMBER_NO'].duplicated().sum()

0

eda.info()

<class 'pandas.core.frame.DataFrame'>
RangeIndex: 62988 entries, 0 to 62987
Data columns (total 23 columns):
 #   Column             Non-Null Count  Dtype  
---  ------             --------------  -----  
 0   MEMBER_NO          62988 non-null  int64  
 1   FFP_DATE           62988 non-null  object 
 2   FIRST_FLIGHT_DATE  62988 non-null  object 
 3   GENDER             62985 non-null  object 
 4   FFP_TIER           62988 non-null  int64  
 5   WORK_CITY          60719 non-null  object 
 6   WORK_PROVINCE      59740 non-null  object 
 7   WORK_COUNTRY       62962 non-null  object 
 8   AGE                62568 non-null  float64
 9   LOAD_TIME          62988 non-null  object 
 10  FLIGHT_COUNT       62988 non-null  int64  
 11  BP_SUM             62988 non-null  int64  
 12  SUM_YR_1           62437 non-null  float64
 13  SUM_YR_2           62850 non-null  float64
 14  SEG_KM_SUM         62988 non-null  int64  
 15  LAST_FLIGHT_DATE   62988 non-null  object 
 16  LAST_TO_END        62988 non-null  int64  
 17  AVG_INTERVAL       62988 non-null  float64
 18  MAX_INTERVAL       62988 non-null  int64  
 19  EXCHANGE_COUNT     62988 non-null  int64  
 20  avg_discount       62988 non-null  float64
 21  Points_Sum         62988 non-null  int64  
 22  Point_NotFlight    62988 non-null  int64  
dtypes: float64(5), int64(10), object(8)
memory usage: 11.1+ MB

eda['LAST_FLIGHT_DATE_NEW'] = np.where(eda['LAST_FLIGHT_DATE']=='2014/2/29  0:00:00', '2014/2/28',eda['LAST_FLIGHT_DATE'])
eda[['FFP_DATE', 'FIRST_FLIGHT_DATE', 'LOAD_TIME','LAST_FLIGHT_DATE_NEW']] = eda[['FFP_DATE', 'FIRST_FLIGHT_DATE', 'LOAD_TIME', 'LAST_FLIGHT_DATE_NEW']].apply(pd.to_datetime)

#Drop variabel LAST_FLIGHT_DATE
eda = eda.drop('LAST_FLIGHT_DATE', axis=1)

eda.info()

<class 'pandas.core.frame.DataFrame'>
RangeIndex: 62988 entries, 0 to 62987
Data columns (total 23 columns):
 #   Column                Non-Null Count  Dtype         
---  ------                --------------  -----         
 0   MEMBER_NO             62988 non-null  int64         
 1   FFP_DATE              62988 non-null  datetime64[ns]
 2   FIRST_FLIGHT_DATE     62988 non-null  datetime64[ns]
 3   GENDER                62985 non-null  object        
 4   FFP_TIER              62988 non-null  int64         
 5   WORK_CITY             60719 non-null  object        
 6   WORK_PROVINCE         59740 non-null  object        
 7   WORK_COUNTRY          62962 non-null  object        
 8   AGE                   62568 non-null  float64       
 9   LOAD_TIME             62988 non-null  datetime64[ns]
 10  FLIGHT_COUNT          62988 non-null  int64         
 11  BP_SUM                62988 non-null  int64         
 12  SUM_YR_1              62437 non-null  float64       
 13  SUM_YR_2              62850 non-null  float64       
 14  SEG_KM_SUM            62988 non-null  int64         
 15  LAST_TO_END           62988 non-null  int64         
 16  AVG_INTERVAL          62988 non-null  float64       
 17  MAX_INTERVAL          62988 non-null  int64         
 18  EXCHANGE_COUNT        62988 non-null  int64         
 19  avg_discount          62988 non-null  float64       
 20  Points_Sum            62988 non-null  int64         
 21  Point_NotFlight       62988 non-null  int64         
 22  LAST_FLIGHT_DATE_NEW  62988 non-null  datetime64[ns]
dtypes: datetime64[ns](4), float64(5), int64(10), object(4)
memory usage: 11.1+ MB

categoric = eda.select_dtypes(include = 'object')
date = eda.select_dtypes(include = 'datetime64[ns]')
numeric = eda.select_dtypes(exclude = ('object','datetime64[ns]'))

categoric.describe()

	GENDER	WORK_CITY	WORK_PROVINCE	WORK_COUNTRY
count	62985	60719	59740	62962
unique	2	3234	1165	118
top	Male	guangzhou	guangdong	CN
freq	48134	9386	17509	57748

date.describe()

	FFP_DATE	FIRST_FLIGHT_DATE	LOAD_TIME	LAST_FLIGHT_DATE_NEW
count	62988	62988	62988	62988
unique	3068	3406	1	730
top	2011-01-13 00:00:00	2013-02-16 00:00:00	2014-03-31 00:00:00	2014-03-31 00:00:00
freq	184	96	62988	959
first	2004-11-01 00:00:00	1905-12-31 00:00:00	2014-03-31 00:00:00	2012-04-01 00:00:00
last	2013-03-31 00:00:00	2015-05-30 00:00:00	2014-03-31 00:00:00	2014-03-31 00:00:00

numeric.describe().T

	count	mean	std	min	25%	50%	75%	max
MEMBER_NO	62988.0	31494.500000	18183.213715	1.0	15747.750000	31494.500000	47241.250000	62988.0
FFP_TIER	62988.0	4.102162	0.373856	4.0	4.000000	4.000000	4.000000	6.0
AGE	62568.0	42.476346	9.885915	6.0	35.000000	41.000000	48.000000	110.0
FLIGHT_COUNT	62988.0	11.839414	14.049471	2.0	3.000000	7.000000	15.000000	213.0
BP_SUM	62988.0	10925.081254	16339.486151	0.0	2518.000000	5700.000000	12831.000000	505308.0
SUM_YR_1	62437.0	5355.376064	8109.450147	0.0	1003.000000	2800.000000	6574.000000	239560.0
SUM_YR_2	62850.0	5604.026014	8703.364247	0.0	780.000000	2773.000000	6845.750000	234188.0
SEG_KM_SUM	62988.0	17123.878691	20960.844623	368.0	4747.000000	9994.000000	21271.250000	580717.0
LAST_TO_END	62988.0	176.120102	183.822223	1.0	29.000000	108.000000	268.000000	731.0
AVG_INTERVAL	62988.0	67.749788	77.517866	0.0	23.370370	44.666667	82.000000	728.0
MAX_INTERVAL	62988.0	166.033895	123.397180	0.0	79.000000	143.000000	228.000000	728.0
EXCHANGE_COUNT	62988.0	0.319775	1.136004	0.0	0.000000	0.000000	0.000000	46.0
avg_discount	62988.0	0.721558	0.185427	0.0	0.611997	0.711856	0.809476	1.5
Points_Sum	62988.0	12545.777100	20507.816700	0.0	2775.000000	6328.500000	14302.500000	985572.0
Point_NotFlight	62988.0	2.728155	7.364164	0.0	0.000000	0.000000	1.000000	140.0

Univariate Analysis

fig, ax = plt.subplots(3,5,figsize=(18, 15))
fig.suptitle('Distribusi Kolom Numeric', fontsize=20)
ax = ax.flatten()
for i,c in enumerate(numeric):
  sns.boxplot(y=c, data=eda, ax=ax[i])
  ax[i].set_title(c) 
  ax[i].set_ylabel('')
plt.show()

fig, ax = plt.subplots(3,5,figsize=(18, 15))
fig.suptitle('Density Kolom Numeric', fontsize=20)
ax = ax.flatten()

for i,c in enumerate(numeric):
  sns.kdeplot(eda[c], linewidth= 1,ax=ax[i])

plt.show()

fig, ax = plt.subplots(1,1,figsize=(8, 6))
fig.suptitle('Distribusi Kolom Gender', fontsize=20)
sns.countplot(x= 'GENDER', data=eda)
plt.xlabel(c);
plt.show()

work = ['WORK_COUNTRY', 'WORK_PROVINCE', 'WORK_CITY']

for i in range(0,len(work)):
    plt.rcParams['figure.figsize'] = (12,5)
    sns.set(font_scale=1.2)
    x = pd.DataFrame(eda[work[i]].value_counts(ascending=True)).tail(15)
    x.plot(kind='barh')
    plt.title('TOP 15 ' + work[i])
    plt.ylabel(work[i])
    plt.xlabel('Frekuensi')
    plt.show()
    print()

# your code goes here!
ffp = eda.groupby(['FFP_DATE']).agg({'MEMBER_NO':['nunique']}).reset_index()
ffp.columns = ['FFP_DATE','Frekuensi']

first = eda.groupby(['FIRST_FLIGHT_DATE']).agg({'MEMBER_NO':['nunique']}).reset_index()
first.columns = ['FIRST_FLIGHT_DATE','Frekuensi']

last = eda.groupby(['LAST_FLIGHT_DATE_NEW']).agg({'MEMBER_NO':['nunique']}).reset_index()
last.columns = ['LAST_FLIGHT_DATE_NEW','Frekuensi']

plt.rcParams['figure.figsize'] = (25,20)
sns.set(font_scale=1.4)

plt.subplot(4, 1, 1)
sns.lineplot(ffp['FFP_DATE'],ffp['Frekuensi'],palette="tab10", linewidth=2.5)
plt.title('FFP_DATE')
plt.show()
print()

plt.subplot(4, 1, 2)
sns.lineplot(first['FIRST_FLIGHT_DATE'],first['Frekuensi'],palette="tab10", linewidth=2.5)
plt.title('FIRST_FLIGHT_DATE')
plt.show()
print()

plt.subplot(4, 1, 3)
sns.lineplot(last['LAST_FLIGHT_DATE_NEW'],last['Frekuensi'],palette="tab10", linewidth=2.5)
plt.title('LAST_FLIGHT_DATE_NEW')
plt.show()

Preprocessing

Handling Missing Values

dfp = eda.copy()

# Checking null values
dfp.isna().sum()

MEMBER_NO                  0
FFP_DATE                   0
FIRST_FLIGHT_DATE          0
GENDER                     3
FFP_TIER                   0
WORK_CITY               2269
WORK_PROVINCE           3248
WORK_COUNTRY              26
AGE                      420
LOAD_TIME                  0
FLIGHT_COUNT               0
BP_SUM                     0
SUM_YR_1                 551
SUM_YR_2                 138
SEG_KM_SUM                 0
LAST_TO_END                0
AVG_INTERVAL               0
MAX_INTERVAL               0
EXCHANGE_COUNT             0
avg_discount               0
Points_Sum                 0
Point_NotFlight            0
LAST_FLIGHT_DATE_NEW       0
dtype: int64

Sebelum dilakukan pengisian data pada Missing Value, akan dicek terlebih dahulu distribusi pada tiap variabel numerik

numer = ['AGE', 'SUM_YR_1','SUM_YR_2']
for i in range(0, len(numer)):
  plt.rcParams['figure.figsize'] = (10,3)
  plt.subplot(1,3,i+1)
  sns.kdeplot(x=dfp[numer[i]], color='blue')
  plt.xlabel(numer[i])
  plt.tight_layout()

Pada variabel numerik yang terdapat missing value memiliki distribusi positively skewed sehingga dalam mengisi missing value akan digunakan Median.

Untuk missing value pada variabel kategorik akan diisi dengan Modus

dfp['AGE'] = dfp['AGE'].fillna(dfp['AGE'].median())
dfp['SUM_YR_1'] = dfp['SUM_YR_1'].fillna(dfp['SUM_YR_1'].median())
dfp['SUM_YR_2'] = dfp['SUM_YR_1'].fillna(dfp['SUM_YR_2'].median())
dfp['GENDER'] = dfp['GENDER'].fillna(dfp['GENDER'].mode()[0])
dfp['WORK_CITY'] = dfp['WORK_CITY'].fillna(dfp['WORK_CITY'].mode()[0])
dfp['WORK_PROVINCE'] = dfp['WORK_PROVINCE'].fillna(dfp['WORK_PROVINCE'].mode()[0])
dfp['WORK_COUNTRY'] = dfp['WORK_COUNTRY'].fillna(dfp['WORK_COUNTRY'].mode()[0])

dfp.isna().sum()

MEMBER_NO               0
FFP_DATE                0
FIRST_FLIGHT_DATE       0
GENDER                  0
FFP_TIER                0
WORK_CITY               0
WORK_PROVINCE           0
WORK_COUNTRY            0
AGE                     0
LOAD_TIME               0
FLIGHT_COUNT            0
BP_SUM                  0
SUM_YR_1                0
SUM_YR_2                0
SEG_KM_SUM              0
LAST_TO_END             0
AVG_INTERVAL            0
MAX_INTERVAL            0
EXCHANGE_COUNT          0
avg_discount            0
Points_Sum              0
Point_NotFlight         0
LAST_FLIGHT_DATE_NEW    0
dtype: int64

plt.figure(figsize = (14,10))
sns.heatmap(dfp.corr(), cmap='Blues', annot=True, fmt='.2f')
plt.tight_layout()

Features Engineering

pd.set_option('display.max_columns', None)
dfp.head(10)

	MEMBER_NO	FFP_DATE	FIRST_FLIGHT_DATE	GENDER	FFP_TIER	WORK_CITY	WORK_PROVINCE	WORK_COUNTRY	AGE	LOAD_TIME	FLIGHT_COUNT	BP_SUM	SUM_YR_1	SUM_YR_2	SEG_KM_SUM	LAST_TO_END	AVG_INTERVAL	MAX_INTERVAL	EXCHANGE_COUNT	avg_discount	Points_Sum	Point_NotFlight	LAST_FLIGHT_DATE_NEW
0	54993	2006-11-02	2008-12-24	Male	6	.	beijing	CN	31.0	2014-03-31	210	505308	239560.0	239560.0	580717	1	3.483254	18	34	0.961639	619760	50	2014-03-31
1	28065	2007-02-19	2007-08-03	Male	6	guangzhou	beijing	CN	42.0	2014-03-31	140	362480	171483.0	171483.0	293678	7	5.194245	17	29	1.252314	415768	33	2014-03-25
2	55106	2007-02-01	2007-08-30	Male	6	.	beijing	CN	40.0	2014-03-31	135	351159	163618.0	163618.0	283712	11	5.298507	18	20	1.254676	406361	26	2014-03-21
3	21189	2008-08-22	2008-08-23	Male	5	Los Angeles	CA	US	64.0	2014-03-31	23	337314	116350.0	116350.0	281336	97	27.863636	73	11	1.090870	372204	12	2013-12-26
4	39546	2009-04-10	2009-04-15	Male	6	guiyang	guizhou	CN	48.0	2014-03-31	152	273844	124560.0	124560.0	309928	5	4.788079	47	27	0.970658	338813	39	2014-03-27
5	56972	2008-02-10	2009-09-29	Male	6	guangzhou	guangdong	CN	64.0	2014-03-31	92	313338	112364.0	112364.0	294585	79	7.043956	52	10	0.967692	343121	15	2014-01-13
6	44924	2006-03-22	2006-03-29	Male	6	wulumuqishi	xinjiang	CN	46.0	2014-03-31	101	248864	120500.0	120500.0	287042	1	7.190000	28	20	0.965347	298873	29	2014-03-31
7	22631	2010-04-09	2010-04-09	Female	6	wenzhoushi	zhejiang	CN	50.0	2014-03-31	73	301864	82440.0	82440.0	287230	3	10.111111	45	7	0.962070	351198	14	2014-03-29
8	32197	2011-06-07	2011-07-01	Male	5	DRANCY	guangdong	FR	50.0	2014-03-31	56	262958	72596.0	72596.0	321489	6	13.054545	94	5	0.828478	295158	7	2014-03-26
9	31645	2010-07-05	2010-07-05	Female	6	wenzhou	zhejiang	CN	43.0	2014-03-31	64	204855	85258.0	85258.0	375074	15	11.333333	73	13	0.708010	251907	16	2014-03-17

LRFM = dfp[['LAST_TO_END','FLIGHT_COUNT','SEG_KM_SUM']].reset_index()

# Membuat indikator L dengan berdasarkan kolom LOAD_TIME dikurangi FPP_DATE
LRFM['L'] = (dfp['LOAD_TIME'] - dfp['FFP_DATE']).dt.days

# Mengubah nama kolom agar sesuai dengan RFM
LRFM.rename(columns={'LAST_TO_END':'R','FLIGHT_COUNT':'F','SEG_KM_SUM':'M'}, inplace = True)

# Membuat ulang judul menjadi LRFM
ColumnsTitles = ['L', 'R', 'F', 'M']
LRFM = LRFM.reindex(columns=ColumnsTitles)
LRFM

	L	R	F	M
0	2706	1	210	580717
1	2597	7	140	293678
2	2615	11	135	283712
3	2047	97	23	281336
4	1816	5	152	309928
...	...	...	...	...
62983	1046	297	2	1134
62984	1484	89	4	8016
62985	2923	29	2	2594
62986	418	400	2	3934
62987	407	403	2	4222

62988 rows × 4 columns

LRFM.describe()

	L	R	F	M
count	62988.000000	62988.000000	62988.000000	62988.000000
mean	1485.000826	176.120102	11.839414	17123.878691
std	847.222941	183.822223	14.049471	20960.844623
min	365.000000	1.000000	2.000000	368.000000
25%	732.000000	29.000000	3.000000	4747.000000
50%	1270.000000	108.000000	7.000000	9994.000000
75%	2179.000000	268.000000	15.000000	21271.250000
max	3437.000000	731.000000	213.000000	580717.000000

for i in LRFM:
    LRFM[i] = np.log(LRFM[i])

LRFM.describe()

	L	R	F	M
count	62988.000000	62988.000000	62988.000000	62988.000000
mean	7.122734	4.367487	1.991248	9.230562
std	0.622567	1.542762	0.952441	1.019778
min	5.899897	0.000000	0.693147	5.908083
25%	6.595781	3.367296	1.098612	8.465268
50%	7.146772	4.682131	1.945910	9.209740
75%	7.686621	5.590987	2.708050	9.965112
max	8.142354	6.594413	5.361292	13.272019

plt.figure(figsize=(15,8))

feat_num = list(LRFM)
for i in range(0, len(feat_num)):
  plt.subplot(1, 7, i+1)
  sns.boxplot(y=LRFM[feat_num[i]],color='teal', orient='v')
  plt.tight_layout()

from scipy import stats

lrfm = LRFM.copy()
print(f'Jumlah baris sebelum memfilter outlier: {len(lrfm)}')

filtered_entries = np.array([True] * len(lrfm))

for col in lrfm:
    zscore = abs(stats.zscore(lrfm[col])) # hitung absolute z-scorenya
    filtered_entries = (zscore < 3) & filtered_entries # keep yang kurang dari 3 absolute z-scorenya
    
lrfm = lrfm[filtered_entries] # filter, cuma ambil yang z-scorenya dibawah 3

print(f'Jumlah baris setelah memfilter outlier: {len(lrfm)}')

Jumlah baris sebelum memfilter outlier: 62988
Jumlah baris setelah memfilter outlier: 62909

plt.figure(figsize=(15,8))

feat_num = list(lrfm)
for i in range(0, len(feat_num)):
  plt.subplot(1, 7, i+1)
  sns.boxplot(y=lrfm[feat_num[i]],color='teal', orient='v')
  plt.tight_layout()

lrfm.duplicated().sum()

103

from sklearn.preprocessing import StandardScaler
sc = StandardScaler()
df_std = sc.fit_transform(lrfm.astype(float))

df_std = pd.DataFrame(data=df_std, columns=lrfm.columns)
df_std.head()

	L	R	F	M
0	1.259228	-2.122596	2.929734	2.828261
1	0.143365	-1.572734	2.765869	2.787433
2	1.374552	-2.385726	2.285287	2.770850
3	0.824086	-1.935902	2.816766	2.757695
4	-0.300310	-1.672771	1.207292	3.004202

df_std.describe()

	L	R	F	M
count	6.290900e+04	6.290900e+04	6.290900e+04	6.290900e+04
mean	2.043623e-15	8.411498e-16	1.361505e-13	-1.485044e-15
std	1.000008e+00	1.000008e+00	1.000008e+00	1.000008e+00
min	-1.963727e+00	-2.835551e+00	-1.365376e+00	-2.999569e+00
25%	-8.458378e-01	-6.283112e-01	-9.382756e-01	-7.526727e-01
50%	3.802738e-02	2.029631e-01	-4.576702e-02	-1.987076e-02
75%	9.057863e-01	7.927738e-01	7.570398e-01	7.230494e-01
max	1.638628e+00	1.443957e+00	3.007158e+00	3.013211e+00

Modeling

inertia = []
silhouette = []
for i in range(2, 11):
    kmeans = KMeans(n_clusters=i, random_state=42)
    kmeans.fit(df_std.values)
    inertia.append(kmeans.inertia_)
    silhouette.append(silhouette_score(df_std, kmeans.labels_))

Elbow Method

fig, ax = plt.subplots(figsize=(10, 6))
sns.lineplot(x=range(2,11), y=inertia, linewidth=2)
sns.scatterplot(x=range(2,11), y=inertia, s=300, color='#800000')
plt.xlabel('Number of clusters, k')
plt.ylabel('Inertia')
plt.xticks(range(2,11))
plt.style.use('ggplot')
plt.title('What is the Best Number for KMeans ?')
plt.show()

inertia

[147613.3431559614,
 118624.34548327875,
 98386.28525706459,
 84659.63522448642,
 75767.59635777943,
 68257.97849250527,
 63075.135949082774,
 59078.83793120229,
 55546.16811277541]

(pd.Series(inertia)-pd.Series(inertia).shift(-1)) / pd.Series(inertia) * 100

0    19.638467
1    17.060630
2    13.951792
3    10.503280
4     9.911385
5     7.593021
6     6.335774
7     5.979586
8          NaN
dtype: float64

Silhoutte

print(silhouette)

plt.figure(figsize=(20, 10))

sns.lineplot(x=range(2, 11), y=silhouette, color='purple', linewidth = 4)
sns.scatterplot(x=range(2, 11), y=silhouette, s=300, color='red',  linestyle='--')
plt.title('Silhouette Score');

[0.3484489838175218, 0.2878397049105127, 0.2762801353190638, 0.26145918627756437, 0.2701074338634501, 0.26678190280219105, 0.24891454853372103, 0.251944247443654, 0.24053811849896609]

K-Means

kmeans = KMeans(n_clusters= 4, random_state=42)
kmeans.fit(df_std)

KMeans(n_clusters=4, random_state=42)

df_std['clusters'] = kmeans.labels_
df_std.sample(5)

	L	R	F	M	clusters
35724	-0.012117	0.606080	-0.635243	-0.375932	3
20402	-1.284740	0.593035	0.218957	0.613204	2
14593	-1.613204	-0.924729	0.430335	0.933470	2
29605	-0.433849	-0.116634	0.218957	-0.052083	2
26471	-0.269356	0.184681	0.521990	0.359318	2

import pandas as pd
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D

# create a 3D scatter plot for L, R, and F with cluster as color
fig = plt.figure(figsize=(10,12))
ax = fig.add_subplot(111, projection='3d')
scatter = ax.scatter(df_std['L'], df_std['R'], df_std['F'], c=df_std['clusters'], cmap='viridis')
ax.set_xlabel('L')
ax.set_ylabel('R')
ax.set_zlabel('F')
plt.colorbar(scatter)
plt.show()

# create a 3D scatter plot for L, R, and M with cluster as color
fig = plt.figure(figsize=(10,12))
ax = fig.add_subplot(111, projection='3d')
scatter = ax.scatter(df_std['L'], df_std['R'], df_std['M'], c=df_std['clusters'], cmap='coolwarm')
ax.set_xlabel('L')
ax.set_ylabel('R')
ax.set_zlabel('M')
plt.colorbar(scatter)
plt.show()

# create a 3D scatter plot for L, F, and M with cluster as color
fig = plt.figure(figsize=(10,12))
ax = fig.add_subplot(111, projection='3d')
scatter = ax.scatter(df_std['L'], df_std['F'], df_std['M'], c=df_std['clusters'], cmap='Pastel1')
ax.set_xlabel('L')
ax.set_ylabel('F')
ax.set_zlabel('M')
plt.colorbar(scatter)
plt.show()

# create a 3D scatter plot for R, F, and M with cluster as color
fig = plt.figure(figsize=(10,12))
ax = fig.add_subplot(111, projection='3d')
scatter = ax.scatter(df_std['R'], df_std['F'], df_std['M'], c=df_std['clusters'], cmap='Spectral')
ax.set_xlabel('R')
ax.set_ylabel('F')
ax.set_zlabel('M')
plt.colorbar(scatter)
plt.show()

PCA

X = df_std.drop('clusters', axis = 1)
y = df_std['clusters']

pca = PCA(n_components=2)

pca.fit(X)
pcs = pca.transform(X)

data_pca = pd.DataFrame(data = pcs, columns = ['PC 1', 'PC 2'])
data_pca.head()

	PC 1	PC 2
0	4.747553	-0.329398
1	4.133231	0.655563
2	4.472706	-0.466240
3	4.459162	0.048785
4	3.274680	0.984055

print('Explained variance:', pca.explained_variance_)
print('Explained variance ratio:', pca.explained_variance_ratio_)

Explained variance: [2.39656635 0.94394264]
Explained variance ratio: [0.59913206 0.23598191]

pca.explained_variance_ratio_.sum() * 100

83.51139723186803

data_pca['Cluster'] = y

fig, ax = plt.subplots(figsize=(15,10))

sns.scatterplot(
    x="PC 1", y="PC 2",
    hue="Cluster",
    edgecolor='black',
    linestyle='--',
    data=data_pca,
    palette= ['blue', 'orange', 'green', 'red'],
    s=160,
    ax=ax
)

<AxesSubplot:xlabel='PC 1', ylabel='PC 2'>

Interpretation

Descriptive Statistics

df_final = df.copy()

df_final['Cluster'] = y

pd.set_option('display.max_columns', None)
df_final.sample(5)

	MEMBER_NO	FFP_DATE	FIRST_FLIGHT_DATE	GENDER	FFP_TIER	WORK_CITY	WORK_PROVINCE	WORK_COUNTRY	AGE	LOAD_TIME	FLIGHT_COUNT	BP_SUM	SUM_YR_1	SUM_YR_2	SEG_KM_SUM	LAST_FLIGHT_DATE	LAST_TO_END	AVG_INTERVAL	MAX_INTERVAL	EXCHANGE_COUNT	avg_discount	Points_Sum	Point_NotFlight	Cluster
59987	3485	11/3/2008	6/15/2012	Male	4	shanghai	shanghai	CN	40.0	3/31/2014	3	692	400.0	0.0	3787	7/1/2012	640	8.000000	9	0	0.332585	692	0	0.0
7003	27881	6/18/2006	6/18/2006	Male	4	beijing	beijing	CN	45.0	3/31/2014	17	28394	3500.0	20429.0	34840	3/23/2014	9	38.687500	210	0	0.798414	28394	0	1.0
42288	8458	1/16/2006	1/16/2006	Male	4	shanghai	shanghai	CN	42.0	3/31/2014	4	3425	1440.0	0.0	4992	10/24/2012	525	63.000000	107	0	0.832632	3425	0	3.0
8578	42201	12/23/2011	12/23/2011	Male	4	guangzhou	guangdong	CN	33.0	3/31/2014	23	21717	13313.0	10337.0	35082	11/10/2013	143	25.909091	146	0	0.696093	28576	12	1.0
51524	23894	9/2/2012	9/2/2012	Male	4	huhehaote	neimenggu	CN	47.0	3/31/2014	3	1274	1740.0	0.0	4111	10/19/2012	530	23.500000	42	0	0.613403	1274	0	3.0

Cluster 0

df_final[df_final['Cluster'] == 0].describe(include=[np.number]).T

	count	mean	std	min	25%	50%	75%	max
MEMBER_NO	14886.0	31362.059317	18159.178866	6.000000	15717.250000	31444.000000	47009.750000	62979.0
FFP_TIER	14886.0	4.012159	0.139291	4.000000	4.000000	4.000000	4.000000	6.0
AGE	14764.0	41.462070	10.211188	6.000000	34.000000	40.000000	48.000000	92.0
FLIGHT_COUNT	14886.0	3.788056	2.616019	2.000000	2.000000	3.000000	5.000000	68.0
BP_SUM	14886.0	2487.673116	1977.567567	0.000000	1220.000000	2030.500000	3227.500000	30413.0
SUM_YR_1	14577.0	1501.169671	1676.834829	0.000000	0.000000	1182.000000	2215.000000	36602.0
SUM_YR_2	14807.0	1299.893429	1559.771774	0.000000	0.000000	908.000000	1989.500000	22586.0
SEG_KM_SUM	14886.0	4794.663980	3291.816829	486.000000	2631.000000	4008.000000	5967.000000	39525.0
LAST_TO_END	14886.0	268.675467	204.499830	1.000000	90.000000	222.000000	426.000000	730.0
AVG_INTERVAL	14886.0	94.865872	106.305381	0.000000	18.500000	64.800000	128.000000	720.0
MAX_INTERVAL	14886.0	161.923082	150.074997	0.000000	27.000000	131.000000	250.000000	720.0
EXCHANGE_COUNT	14886.0	0.047158	0.319019	0.000000	0.000000	0.000000	0.000000	13.0
avg_discount	14886.0	0.672094	0.190481	0.112043	0.540002	0.670028	0.796892	1.5
Points_Sum	14886.0	3178.789870	4312.555086	0.000000	1340.250000	2276.000000	3723.750000	235494.0
Point_NotFlight	14886.0	1.870012	5.841079	0.000000	0.000000	0.000000	0.000000	66.0
Cluster	14886.0	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.0

df_final[df_final['Cluster'] == 0].describe(include=[object]).T

	count	unique	top	freq
FFP_DATE	14886	2809	1/13/2011	73
FIRST_FLIGHT_DATE	14886	3007	2/16/2013	35
GENDER	14886	2	Male	10803
WORK_CITY	14315	1236	beijing	1989
WORK_PROVINCE	14057	450	guangdong	3768
WORK_COUNTRY	14877	73	CN	13670
LOAD_TIME	14886	1	3/31/2014	14886
LAST_FLIGHT_DATE	14886	730	2/17/2014	78

Cluster 1

df_final[df_final['Cluster'] == 1].describe(include=[np.number]).T

	count	mean	std	min	25%	50%	75%	max
MEMBER_NO	15119.0	31478.184338	18242.523686	3.000000	15505.000000	31417.000000	47334.000000	62988.0
FFP_TIER	15119.0	4.317349	0.604661	4.000000	4.000000	4.000000	4.000000	6.0
AGE	15047.0	43.917193	9.516382	12.000000	37.000000	43.000000	50.000000	89.0
FLIGHT_COUNT	15119.0	26.059065	19.841308	2.000000	13.000000	21.000000	33.000000	213.0
BP_SUM	15119.0	27132.119585	25241.852177	0.000000	12723.000000	19878.000000	32775.500000	505308.0
SUM_YR_1	15115.0	12555.927092	12589.161217	0.000000	4885.000000	9300.000000	16109.500000	239560.0
SUM_YR_2	15117.0	13705.575246	13292.029656	0.000000	5547.000000	10181.000000	17604.000000	234188.0
SEG_KM_SUM	15119.0	39602.649117	29627.668450	2272.000000	20671.000000	31400.000000	49234.000000	580717.0
LAST_TO_END	15119.0	75.814604	106.396548	1.000000	11.000000	32.000000	97.000000	711.0
AVG_INTERVAL	15119.0	35.167604	29.375225	0.000000	18.448684	28.105263	42.500000	656.0
MAX_INTERVAL	15119.0	141.004895	81.760130	0.000000	83.000000	123.000000	178.000000	678.0
EXCHANGE_COUNT	15119.0	0.904425	1.934277	0.000000	0.000000	0.000000	1.000000	46.0
avg_discount	15119.0	0.780532	0.185494	0.350275	0.672505	0.745214	0.830586	1.5
Points_Sum	15119.0	30758.243733	31460.262713	0.000000	13462.000000	21522.000000	36543.500000	795398.0
Point_NotFlight	15119.0	4.649845	9.781602	0.000000	0.000000	1.000000	4.000000	140.0
Cluster	15119.0	1.000000	0.000000	1.000000	1.000000	1.000000	1.000000	1.0

df_final[df_final['Cluster'] == 1].describe(include=[object]).T

	count	unique	top	freq
FFP_DATE	15119	2968	9/9/2005	34
FIRST_FLIGHT_DATE	15119	3072	9/9/2005	29
GENDER	15118	2	Male	12267
WORK_CITY	14645	1269	guangzhou	2966
WORK_PROVINCE	14441	470	guangdong	4962
WORK_COUNTRY	15115	53	CN	13817
LOAD_TIME	15119	1	3/31/2014	15119
LAST_FLIGHT_DATE	15119	596	3/31/2014	494

Cluster 2

df_final[df_final['Cluster'] == 2].describe(include=[np.number]).T

	count	mean	std	min	25%	50%	75%	max
MEMBER_NO	14800.0	31785.760676	18222.260233	1.000000	15961.500000	31709.000000	47692.500000	62987.0
FFP_TIER	14800.0	4.068716	0.301708	4.000000	4.000000	4.000000	4.000000	6.0
AGE	14706.0	42.833129	9.686232	7.000000	36.000000	42.000000	48.000000	110.0
FLIGHT_COUNT	14800.0	12.595000	9.446613	2.000000	6.000000	10.000000	16.000000	101.0
BP_SUM	14800.0	10765.692905	8616.043729	0.000000	5754.000000	8591.500000	13129.750000	208801.0
SUM_YR_1	14780.0	5332.259202	5145.395749	0.000000	2003.750000	4288.000000	7234.250000	125188.0
SUM_YR_2	14795.0	5636.167219	5602.287243	0.000000	2107.000000	4419.000000	7542.000000	109401.0
SEG_KM_SUM	14800.0	17762.972770	12107.106022	1102.000000	9921.000000	14732.500000	21914.750000	184227.0
LAST_TO_END	14800.0	132.112297	145.967782	1.000000	25.000000	79.500000	186.000000	730.0
AVG_INTERVAL	14800.0	55.959481	45.146354	0.000000	30.060033	45.153846	68.166667	658.0
MAX_INTERVAL	14800.0	180.156824	105.832820	0.000000	107.000000	160.000000	232.000000	719.0
EXCHANGE_COUNT	14800.0	0.274392	0.862329	0.000000	0.000000	0.000000	0.000000	20.0
avg_discount	14800.0	0.738002	0.167601	0.136017	0.635504	0.720704	0.806724	1.5
Points_Sum	14800.0	12153.410405	12219.149702	0.000000	6061.750000	9230.000000	14498.000000	647113.0
Point_NotFlight	14800.0	2.520878	6.926826	0.000000	0.000000	0.000000	1.000000	104.0
Cluster	14800.0	2.000000	0.000000	2.000000	2.000000	2.000000	2.000000	2.0

df_final[df_final['Cluster'] == 2].describe(include=[object]).T

	count	unique	top	freq
FFP_DATE	14800	2903	1/1/2013	34
FIRST_FLIGHT_DATE	14800	3034	9/9/2005	27
GENDER	14798	2	Male	11471
WORK_CITY	14275	1265	guangzhou	2201
WORK_PROVINCE	14012	458	guangdong	4077
WORK_COUNTRY	14796	61	CN	13504
LOAD_TIME	14800	1	3/31/2014	14800
LAST_FLIGHT_DATE	14800	686	3/28/2014	267

Cluster 3

df_final[df_final['Cluster'] == 3].describe(include=[np.number]).T

	count	mean	std	min	25%	50%	75%	max
MEMBER_NO	18104.0	31394.665709	18108.038831	5.000000	15785.0000	31408.500000	46892.500000	62983.0
FFP_TIER	18104.0	4.024249	0.195564	4.000000	4.0000	4.000000	4.000000	6.0
AGE	17972.0	41.816771	9.912835	9.000000	34.0000	40.000000	48.000000	92.0
FLIGHT_COUNT	18104.0	6.009611	4.732123	2.000000	3.0000	5.000000	8.000000	72.0
BP_SUM	18104.0	4504.610915	3643.312540	0.000000	2022.7500	3594.000000	5934.000000	42831.0
SUM_YR_1	17892.0	2452.424771	2647.911794	0.000000	630.0000	1831.000000	3495.250000	51014.0
SUM_YR_2	18054.0	2346.753683	2677.841307	0.000000	0.0000	1651.000000	3446.750000	37990.0
SEG_KM_SUM	18104.0	8036.289991	5987.054036	716.000000	3966.0000	6454.000000	10448.000000	89033.0
LAST_TO_END	18104.0	219.186644	192.848598	1.000000	57.0000	161.000000	346.000000	731.0
AVG_INTERVAL	18104.0	82.390628	85.870625	0.000000	31.0000	60.111111	103.525000	728.0
MAX_INTERVAL	18104.0	179.285959	136.936409	0.000000	73.0000	159.000000	259.000000	728.0
EXCHANGE_COUNT	18104.0	0.093239	0.513455	0.000000	0.0000	0.000000	0.000000	27.0
avg_discount	18104.0	0.700782	0.178375	0.157402	0.5852	0.695196	0.800876	1.5
Points_Sum	18104.0	5401.852740	9899.798169	0.000000	2210.0000	3939.000000	6660.250000	985572.0
Point_NotFlight	18104.0	1.996189	6.075219	0.000000	0.0000	0.000000	0.000000	92.0
Cluster	18104.0	3.000000	0.000000	3.000000	3.0000	3.000000	3.000000	3.0

df_final[df_final['Cluster'] == 3].describe(include=[object]).T

	count	unique	top	freq
FFP_DATE	18104	2898	1/1/2013	68
FIRST_FLIGHT_DATE	18104	3130	2/16/2013	33
GENDER	18104	2	Male	13539
WORK_CITY	17411	1367	beijing	2462
WORK_PROVINCE	17164	486	guangdong	4668
WORK_COUNTRY	18095	64	CN	16691
LOAD_TIME	18104	1	3/31/2014	18104
LAST_FLIGHT_DATE	18104	728	3/28/2014	142

Visualisation Conclusion

radar_plot = df_std.groupby('clusters').agg('mean').reset_index()
radar_plot

	clusters	L	R	F	M
0	0	-0.897608	0.748526	-0.976778	-0.968333
1	1	0.675290	-1.007530	1.230186	1.152476
2	2	-0.810065	-0.209018	0.367169	0.397506
3	3	0.836337	0.396806	-0.524358	-0.491205

category = ['L', 'R', 'F', 'M']
categories = [*category, category[0]]
color = ['blue', 'orange', 'green', 'red']
clusters = []

for i in range(0,4):
    num = []
    for cat in category:
        num.append(radar_plot[cat][i])
    num.append(radar_plot['L'][i])
    clusters.append(num)

label_loc = np.linspace(start=0, stop=2 * np.pi, num=len(clusters[0]))

plt.figure(figsize=(8, 8))
plt.subplot(polar=True)
for i in range(0,4):
    plt.plot(label_loc, clusters[i], color=color[i], label=f'Cluster {i}')

plt.title('Customer Segmentation', size=20, y=1.05)
lines, labels = plt.thetagrids(np.degrees(label_loc), labels=categories)
plt.yticks([-1,0,1,2], ["-1","0","1","2"], color="grey", size=7)
plt.ylim(-1.5,2.5)
plt.legend()
plt.show()

plt.figure(figsize=(8, 8))
ax = plt.subplot(polar=True)

# Menampilkan garis dan label sumbu theta
lines, labels = plt.thetagrids(np.degrees(label_loc), labels=categories)

# Menampilkan label sumbu radial
plt.yticks([-1,0,1,2], ["-1","0","1","2"], color="grey", size=7)

# Menentukan batas sumbu radial
plt.ylim(-1.5,2.5)

# Menampilkan plot data
plt.plot(label_loc, clusters[0], color=color[0], label = 'Cluster 0')

# Menambahkan teks pada setiap titik data
for i, val in enumerate(clusters[0]):
    angle = label_loc[i]
    radius = val
    score = round(val, 2)
    x = angle
    y = radius + 0.2
    plt.text(x, y, score, ha='center', va='center')

# Menampilkan legenda
plt.legend()

# Menampilkan plot
plt.show()

Cluster 0: Customer pada cluster ini memiliki nilai L (Length of customer relationship) dan F (Flight frequency) yang rendah, dan nilai M (Monetary value) yang sangat rendah. Sementara itu, nilai R (Recency) mereka tergolong tinggi. Oleh karena itu, cluster ini dapat diinterpretasikan sebagai cluster dari customer yang belum lama bergabung dengan jasa penerbangan dan belum melakukan banyak penerbangan, serta memiliki nilai belanja yang rendah.

plt.figure(figsize=(8, 8))
ax = plt.subplot(polar=True)

# Menampilkan garis dan label sumbu theta
lines, labels = plt.thetagrids(np.degrees(label_loc), labels=categories)

# Menampilkan label sumbu radial
plt.yticks([-1,0,1,2], ["-1","0","1","2"], color="grey", size=7)

# Menentukan batas sumbu radial
plt.ylim(-1.5,2.5)

# Menampilkan plot data
plt.plot(label_loc, clusters[1], color=color[1], label = 'Cluster 1')

# Menambahkan teks pada setiap titik data
for i, val in enumerate(clusters[1]):
    angle = label_loc[i]
    radius = val
    score = round(val, 2)
    x = angle
    y = radius + 0.2
    plt.text(x, y, score, ha='center', va='center')

# Menampilkan legenda
plt.legend()

# Menampilkan plot
plt.show()

Cluster 1: Customer pada cluster ini memiliki nilai L (Length of customer relationship) yang relatif tinggi, dan nilai R (Recency) yang rendah, artinya mereka adalah customer yang telah lama menjadi pelanggan jasa penerbangan dan melakukan perjalanan baru-baru ini. Selain itu, nilai F (Flight frequency) dan M (Monetary value) mereka juga relatif tinggi, yang menunjukkan bahwa mereka adalah pelanggan yang sering melakukan perjalanan dan memiliki nilai belanja yang tinggi.

plt.figure(figsize=(8, 8))
ax = plt.subplot(polar=True)

# Menampilkan garis dan label sumbu theta
lines, labels = plt.thetagrids(np.degrees(label_loc), labels=categories)

# Menampilkan label sumbu radial
plt.yticks([-1,0,1,2], ["-1","0","1","2"], color="grey", size=7)

# Menentukan batas sumbu radial
plt.ylim(-1.5,2.5)

# Menampilkan plot data
plt.plot(label_loc, clusters[2], color=color[2], label = 'Cluster 2')

# Menambahkan teks pada setiap titik data
for i, val in enumerate(clusters[2]):
    angle = label_loc[i]
    radius = val
    score = round(val, 2)
    x = angle
    y = radius + 0.2
    plt.text(x, y, score, ha='center', va='center')

# Menampilkan legenda
plt.legend()

# Menampilkan plot
plt.show()

Cluster 2: Customer pada cluster ini memiliki nilai L (Length of customer relationship) dan M (Monetary value) yang sedang, dan nilai R (Recency) yang relatif tinggi. Sementara itu, nilai F (Flight frequency) mereka tergolong rendah. Oleh karena itu, cluster ini dapat diinterpretasikan sebagai cluster dari customer yang sudah lama menjadi pelanggan jasa penerbangan dan memiliki nilai belanja yang sedang, tetapi tidak terlalu sering melakukan perjalanan.

plt.figure(figsize=(8, 8))
ax = plt.subplot(polar=True)

# Menampilkan garis dan label sumbu theta
lines, labels = plt.thetagrids(np.degrees(label_loc), labels=categories)

# Menampilkan label sumbu radial
plt.yticks([-1,0,1,2], ["-1","0","1","2"], color="grey", size=7)

# Menentukan batas sumbu radial
plt.ylim(-1.5,2.5)

# Menampilkan plot data
plt.plot(label_loc, clusters[3], color=color[3], label = 'Cluster 3')

# Menambahkan teks pada setiap titik data
for i, val in enumerate(clusters[3]):
    angle = label_loc[i]
    radius = val
    score = round(val, 2)
    x = angle
    y = radius + 0.2
    plt.text(x, y, score, ha='center', va='center')

# Menampilkan legenda
plt.legend()

# Menampilkan plot
plt.show()

Cluster 3: Customer pada cluster ini memiliki nilai L (Length of customer relationship) yang relatif tinggi, dan nilai R (Recency) yang rendah, artinya mereka adalah customer yang telah lama menjadi pelanggan jasa penerbangan dan melakukan perjalanan baru-baru ini. Namun, nilai F (Flight frequency) dan M (Monetary value) mereka relatif rendah dibandingkan dengan cluster 1. Oleh karena itu, cluster ini dapat diinterpretasikan sebagai cluster dari customer yang lebih jarang melakukan perjalanan, tetapi tetap memiliki nilai belanja yang cukup tinggi.

Recommendation

• Cluster 0: Customer pada cluster ini adalah pelanggan baru yang belum melakukan banyak penerbangan dan memiliki nilai belanja yang rendah. Untuk meningkatkan nilai belanja dari pelanggan pada cluster ini, jasa penerbangan dapat memberikan promo atau diskon untuk pembelian tiket pada waktu-waktu tertentu. Selain itu, jasa penerbangan juga dapat memberikan reward atau poin loyalty program kepada pelanggan yang sering melakukan penerbangan.

• Cluster 1: Customer pada cluster ini adalah pelanggan setia yang sering melakukan penerbangan dan memiliki nilai belanja yang tinggi. Untuk menjaga loyalitas dari pelanggan pada cluster ini, jasa penerbangan dapat memberikan reward yang lebih tinggi atau benefit tambahan pada program loyalty program mereka. Selain itu, jasa penerbangan juga dapat memberikan layanan tambahan seperti lounge khusus atau layanan prioritas pada waktu check-in dan boarding.

• Cluster 2: Customer pada cluster ini adalah pelanggan yang sudah lama menjadi pelanggan jasa penerbangan dan memiliki nilai belanja yang sedang, tetapi tidak terlalu sering melakukan penerbangan. Untuk meningkatkan frekuensi dari penerbangan pada pelanggan pada cluster ini, jasa penerbangan dapat memberikan promo khusus untuk penerbangan-penerbangan tertentu pada waktu-waktu tertentu. Selain itu, jasa penerbangan juga dapat memberikan program diskon atau benefit tambahan pada pelanggan yang sering melakukan penerbangan.

• Cluster 3: Customer pada cluster ini adalah pelanggan setia yang memiliki nilai belanja yang cukup tinggi, tetapi frekuensi penerbangan mereka relatif rendah dibandingkan dengan pelanggan pada cluster 1. Untuk meningkatkan frekuensi dari penerbangan pada pelanggan pada cluster ini, jasa penerbangan dapat memberikan promo khusus atau diskon untuk penerbangan-penerbangan tertentu pada waktu-waktu tertentu. Selain itu, jasa penerbangan juga dapat memberikan program reward atau poin loyalty program kepada pelanggan yang sering melakukan penerbangan.